Skip to main content

Algorithms for triangulated terrains

  • Invited Papers
  • Conference paper
  • First Online:
SOFSEM'97: Theory and Practice of Informatics (SOFSEM 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1338))

Abstract

Digital elevation models can represent many types of geographic data. One of the common digital elevation models is the triangulated irregular network (also called TIN, or polyhedral terrain, or triangulated terrain). We discuss ways to represent a TIN in a data structure, and give some of the basic algorithms that work on TINs. These include retrieving contour lines, computing perspective views, and constructing TINS from other digital elevation data. We also give a recent method to compress and decompress a TIN for storage and transmission purposes.

Research is partially supported by the ESPRIT IV LTR Project No. 21957 (CGAL).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B.P. Buttenfield and W.A. Mackaness. Visualization. In D.J. Maguire, M.F. Goodchild, and D.W. Rhind, editors, Geographical Information Systems — Principles and Applications, volume 1, pages 427–443. Longman Scientific & Technical, 1991.

    Google Scholar 

  2. CGAL home page. http://www.cs.run. nl/CGAL/.

    Google Scholar 

  3. N. Chiba, T. Nishizeki, and N. Saito. A linear 5-coloring algorithm of planar graphs. J. of Algorithms, 2:317–327, 1981.

    Google Scholar 

  4. K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom., 4:387–421, 1989.

    Google Scholar 

  5. M. de Berg. Visualization of TINS. In M. van Kreveld, J. Nievergelt, T. Roos, and P. Widmayer, editors, Algorithmic Foundations of GIS, Lecture Notes in Comp. Science. Springer-Verlag, 1997. to appear.

    Google Scholar 

  6. M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry — Algorithms and Applications. Springer-Verlag, Berlin, 1997.

    Google Scholar 

  7. H. Djidjev and A. Lingas. On computing Voronoi diagrams for sorted point sets. Internat. J. Comput. Geom. Appl., 5:327–337, 1995.

    Google Scholar 

  8. D. P. Dobkin. Computational geometry and computer graphics. Proc. IEEE, 80(9):1400–1411, September 1992.

    Google Scholar 

  9. P.-O. Fjällström. Polyhedral approximation of bivariate functions. In Proc. 3rd Canad. Conf. Comput. Geom., pages 187–190, 1991.

    Google Scholar 

  10. L. De Floriani, D. Mirra, and E. Puppo. Extracting contour lines from a hierarchical surface model. In Eurographics'93, volume 12, pages 249–260, 1993.

    Google Scholar 

  11. Wm Randolph Franklin. Compressing elevation data. In Advances in Spatial Databases (SSD'95), number 951 in Lecture Notes in Computer Science, pages 385–404, Berlin, 1995. Springer-Verlag.

    Google Scholar 

  12. Wm Randolph Franklin and A. Said. Lossy compression elevation data. In Proc. 7th Int. Symp. on Spatial Data Handling, pages 8B.29–813.41, 1996.

    Google Scholar 

  13. L. J. Guibas, D. E. Knuth, and M. Sharir. Randomized incremental construction of Delaunay and Voronoi diagrams. Algorithmica, 7:381–413, 1992.

    Google Scholar 

  14. L. J. Guibas and J. Stolfi. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans. Graph., 4:74–123, 1985.

    Google Scholar 

  15. P. S. Heckbert and M. Garland. Fast polygonal approximation of terrains and height fields. Report CMU-CS-95-181, Carnegie Mellon University, 1995.

    Google Scholar 

  16. M. Heller. Triangulation algorithms for adaptive terrain modeling. In Proc. 4th Int. Symp. on Spatial Data Handling, pages 163–174, 1990.

    Google Scholar 

  17. D. G. Kirkpatrick. Optimal search in planar subdivisions. SIAM J. Comput., 12:28–35, 1983.

    Google Scholar 

  18. A.M. MacEachren and D.R.F. Taylor, editors. Visualization in Modern Cartography. Elsevier Science Inc., New York, 1994.

    Google Scholar 

  19. Atsuyuki Okabe, Barry Boots, and Kokichi Sugihara. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. John Wiley & Sons, Chichester, UK, 1992.

    Google Scholar 

  20. J. O'Rourke. Computational Geometry in C. Cambridge Univ. Press, NY, 1994.

    Google Scholar 

  21. F. P. Preparata and M. I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, New York, NY, 1985.

    Google Scholar 

  22. Relief: depicting a surface on a map. http://acorn.educ.nottingham.ac.uk/ShellCent/maps/relief.html.

    Google Scholar 

  23. N. Robertson, D.P. Sanders, P. Seymour, and R. Thomas. Efficiently four-coloring planar graphs. In Proc. 28th ACM Symp. Theor. Comp., pages 571–575, 1996.

    Google Scholar 

  24. R. Seidel. Backwards analysis of randomized geometric algorithms. In J. Pach, editor, New Trends in Discrete and Computational Geometry, volume 10 of Algorithms and Combinatorics, pages 37–68. Springer-Verlag, 1993.

    Google Scholar 

  25. J. Snoeyink and M. van Kreveld. Good orders for incremental (re) construction. In Proc. 13th ACM Symp. Computational Geometry, pages 400–402, 1997.

    Google Scholar 

  26. J. Snoeyink and M. van Kreveld. Linear time reconstruction of the Delaunay triangulation with applications. In Proc. 7th Europ. Symp. Algorithms, Lecture Notes in Comp. Science. Springer-Verlag, 1997.

    Google Scholar 

  27. S.S. Stevens. On the theory of scales of measurement. Science, 103:677–680, 1946.

    Google Scholar 

  28. M. van Kreveld. Efficient methods for isoline extraction from a TIN. Int. J. of GIS, 10:523–540, 1996.

    Google Scholar 

  29. M. van Kreveld. Digital elevation models and TIN algorithms. In M. van Kreveld, J. Nievergelt, T. Roos, and P. Widmayer, editors, Algorithmic Foundations of GIS, Lecture Notes in Comp. Science. Springer-Verlag, 1997. to appear.

    Google Scholar 

  30. Visualization techniques for landscape evaluation, literature review. http://bamboo.mluri.sari.ac.uk/ jo/litrev/chapters.html.

    Google Scholar 

  31. R. Weibel and M. Heller. Digital terrain modelling. In D. J. Maguire, M. F. Goodchild, and D. W. Rhind, editors, Geographical Information Systems — Principles and Applications, pages 269–297. Longman, London, 1991.

    Google Scholar 

  32. M.F. Worboys. GIS: A Computing Perspective. Taylor & Francis, London, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

František Plášil Keith G. Jeffery

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van Kreveld, M. (1997). Algorithms for triangulated terrains. In: Plášil, F., Jeffery, K.G. (eds) SOFSEM'97: Theory and Practice of Informatics. SOFSEM 1997. Lecture Notes in Computer Science, vol 1338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63774-5_95

Download citation

  • DOI: https://doi.org/10.1007/3-540-63774-5_95

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63774-5

  • Online ISBN: 978-3-540-69645-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics